Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of handwritten notes

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          <head xml:id="echoid-head22" xml:space="preserve">VI.</head>
          <p>
            <s xml:id="echoid-s440" xml:space="preserve">Ambo ſimul latera FL, FH, FIGVRÆ LATERA nuncupantur.</s>
            <s xml:id="echoid-s441" xml:space="preserve"/>
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        <div xml:id="echoid-div22" type="section" level="1" n="18">
          <head xml:id="echoid-head23" xml:space="preserve">VII.</head>
          <p>
            <s xml:id="echoid-s442" xml:space="preserve">Recta verò LV æquidiſtans diametro ſectionis FG, vt & </s>
            <s xml:id="echoid-s443" xml:space="preserve">recta HL, figuræ
              <lb/>
            latera ſub tendens dicitur FIGVRAM DETERMINANS, ſeu REGV-
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            LATRIX, vel REGVLA.</s>
            <s xml:id="echoid-s444" xml:space="preserve"/>
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        <div xml:id="echoid-div23" type="section" level="1" n="19">
          <head xml:id="echoid-head24" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s445" xml:space="preserve">Segmenta inſuper diametrorum NF, GF, licet ab ipſo Apollonio dicantur
              <lb/>
            latitudines, vocentur potius ALTITVDINES, ita vt NF dicatur altitu-
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            do propria ſemi-applicatæ MN &</s>
            <s xml:id="echoid-s446" xml:space="preserve">c.</s>
            <s xml:id="echoid-s447" xml:space="preserve"/>
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        <div xml:id="echoid-div24" type="section" level="1" n="20">
          <head xml:id="echoid-head25" xml:space="preserve">IX.</head>
          <p>
            <s xml:id="echoid-s448" xml:space="preserve">Rectæ autem NX, GV, quæ recto lateri FL, ſiue ordinatim ductis æquidi-
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            ſtant, & </s>
            <s xml:id="echoid-s449" xml:space="preserve">inter ſectionis diametrum, & </s>
            <s xml:id="echoid-s450" xml:space="preserve">regulam intercipiuntur, vocentur
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            LATITVDINES, rectangulorum nempe FNX, FGV, quibus ſemi-ap-
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            plicatarum quadrata NM, GD æqualia ſunt oſtenſa, ita vt XM ſit latitu-
              <lb/>
            do propria ſemi-applicatæ MN &</s>
            <s xml:id="echoid-s451" xml:space="preserve">c. </s>
            <s xml:id="echoid-s452" xml:space="preserve">quæ ſemi-applicatæ indifferenter,
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            ac ſępius dicentur applicatæ, velordinatim ductæ.</s>
            <s xml:id="echoid-s453" xml:space="preserve"/>
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        <div xml:id="echoid-div25" type="section" level="1" n="21">
          <head xml:id="echoid-head26" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s454" xml:space="preserve">HInc patet, in quacunque coni-ſectione, quamlibet ſemi-applicatam
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            eſſe mediam proportionalem inter propriam altitudinem, propriam-
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            que latitudinem: </s>
            <s xml:id="echoid-s455" xml:space="preserve">hoc eſt quadratum cuiuſcunque ſemi-applicatæ æquari
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            rectangulo ſub propria altitudine, ac propria latitudine contento: </s>
            <s xml:id="echoid-s456" xml:space="preserve">oſtenſum
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            eſt enim tàm in Parabola, quàm in Hyperbola, vel Ellipſi, vel circulo, qua-
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            dratum ſemi-applicatæ MN æquari rectangulo FX, quod ſub altitudine
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            propria FN, ac ſub propria latitudine NX continetur.</s>
            <s xml:id="echoid-s457" xml:space="preserve"/>
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        <div xml:id="echoid-div26" type="section" level="1" n="22">
          <head xml:id="echoid-head27" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s458" xml:space="preserve">HIC animaduertendum eſt in hac propoſitione nos ſub contrariam
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            com-ſectionem non excluſiſſe, quam Apollonius in eius quinta
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            primi expendens, circulum eſſe demonſtrauit, quoniam ex eo,
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            quod ſuperius dictum fuit, elicitur huic etiam competere eandem
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            Ellipſis proprietatem, videlicet ordinatè applicatarum potentias æquarire-
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            ctangulis, rectæ lineæ quarto loco inuentæ applicatis, latitudinem habentibus
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            ea diametri ſegmenta, quæ inter ipſas applicatas, ac ſectionis verticem in-
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            tercipiuntur, deficientibuſque rectangulis ſimilibus contento ſub tranſuerſo re-
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            ctoque latere, quæ latera in hac ſub contraria ſectione inter ſe ſunt æqualia, ac
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            penitùs eadem cum diametro vnius circuli: </s>
            <s xml:id="echoid-s459" xml:space="preserve">quamobrem circulus nihil aliud
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            eſſe videtur quàm Ellipſis æqualium laterum, habens tamen tranſuerſum
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            latus, quod vicem gerit axis linearum ad ipſum ordinatè ductarum.</s>
            <s xml:id="echoid-s460" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s461" xml:space="preserve">Immo ſi noſtri eſſet inſtituti, hic quoque demonſtrare poſſemus non </s>
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